Topic 3 Dielectric Waveguides and Optical Fibers 2-1 Symmetric ...

Example 2.3.4: Group velocity and delay
Consider a single mode fiber with core and cladding indices of 1.448
and 1.440, core radius of 3μm, operating at 1.5μm. Given that
we can approximate the fundamental mode normalized
propagation constant b by
901 37500 光電導論
b ≈ (1.1428 – 0.996 / V ) 2 1.5 < V < 2.5
(1) Calculate the propagation constant β.
(2) Change the operating wavelength to λ’ by a small amount,
0.01%, and then recalculate the new propagation constant β’.
(3) Then determine the group velocity v g of the fundamental mode at
1.5μm, and the group delay τ g over 1 km of fiber.
αα max
n 0
901 37500 光電導論
n 2
n 1
θ < θ c
Fiber axis
Lost
B
θ > θ c
Cladding
Core
©1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Propagates
A
37
Maximumacceptance angle
α max is that which just gives
totalinternalreflectionatthe
core-cladding interface, i.e.
when α=α maxthen θ=θ c.
Rays with α>α max (e.g. ray
B) become refracted and
penetrate the cladding and are
eventually lost.
39
901 37500 光電導論
Snell’s law -->
Numerical Aperture
901 37500 光電導論
2-4 Numerical Aperture
Maximum acceptance
angle α max
sinα
max n
=
sin( 90 −θ ) n
sinα
max
=
c
1
0
2 2 ( n − n )
1
n
0
( ) 2 / 1 2 2
n n
NA = −
sinα
max
1
=
0
2
NA
n
2πa
V = NA
λ
1/
2
2
38
40